Lie algebras of finite and affine type / R.W. Carter.

Format:

Book

Author/Creator:

Carter, Roger W. (Roger William), author.

Series:

Cambridge studies in advanced mathematics ; 96.

Cambridge studies in advanced mathematics ; 96

Language:

English

Subjects (All):

Lie algebras.

Physical Description:

1 online resource (xvii, 632 pages) : digital, PDF file(s).

Other Title:

Lie Algebras of Finite & Affine Type

Place of Publication:

Cambridge : Cambridge University Press, 2005.

Language Note:

English

Summary:

Lie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject, including both the Cartan-Killing-Weyl theory of finite dimensional simple algebras and the more modern theory of Kac-Moody algebras. Proofs are given in detail and the only prerequisite is a sound knowledge of linear algebra. The first half of the book deals with classification of the finite dimensional simple Lie algebras and of their finite dimensional irreducible representations. The second half introduces the theory of Kac-Moody algebras, concentrating particularly on those of affine type. A brief account of Borcherds algebras is also included. An Appendix gives a summary of the basic properties of each Lie algebra of finite and affine type.

Contents:

Cover; Half-title; Title; Copyright; Dedication; Contents; Preface; 1 Basic concepts; 2 Representations of soluble and nilpotent Lie algebras; 3 Cartan subalgebras; 4 The Cartan decomposition; 5 The root system and the Weyl group; 6 The Cartan matrix and the Dynkin diagram; 7 The existence and uniqueness theorems; 8 The simple Lie algebras; 9 Some universal constructions; 10 Irreducible modules for semisimple Lie algebras; 11 Further properties of the universal enveloping algebra; 12 Character and dimension formulae; 13 Fundamental modules for simple Lie algebras

14 Generalised Cartan matrices and Kac–Moody algebras15 The classification of generalised Cartan matrices; 16 The invariant form, Weyl group, and root system; 17 Kac–Moody algebras of affine type; 18 Realisations of affine Kac–Moody algebras; 19 Some representations of symmetrisable Kac–Moody algebras; 20 Representations of affine Kac–Moody algebras; 21 Borcherds Lie algebras; Appendix; Notation; Bibliography; Bibliography; Index;

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-15416-2

1-280-43162-8

9786610431625

0-511-18274-0

0-511-13083-X

0-511-20053-6

0-511-30091-3

0-511-61491-8

0-511-12930-0

OCLC:

171137561